Jerome Boateng scored his first international goal to set Germany on its way to a 3-0 win against Slovakia at UEFA Euro 2016 as the world champion cruised into the quarter-finals on Monday (AEST).

Boateng opened his account eight minutes into his 63rd international appearance and Joachim Low's side never looked back against an outclassed opponent.

Mesut Ozil had a penalty saved soon after but Julian Draxler set up Mario Gomez to double the lead two minutes before half-time and the impressive Draxler then completed the scoring just after the hour mark.

There was never any threat of a repeat of Slovakia's 3-1 win when the teams met in a friendly just four weeks ago and Germany moves on to a last-eight tie against either reigning European champion Spain or old rival Italy next weekend.

Low had been unhappy with his team's finishing during the group stage and he opted to drop the underperforming Mario Goetze as Draxler, of Wolfsburg, started in the only change from the 1-0 win against Northern Ireland. 

Slovakia has a recent history of pulling off surprise results, from its defeat of Spain in qualifying to the recent friendly victory in Germany and the goalless draw with England that saw it progress from the group stage. 

But its hopes of another day to remember were rapidly nipped in the bud by the world champion, which underlined its credentials and sent a clear message to its other Euro rivals. 

Sami Khedira was first to threaten with a header from a Toni Kroos free-kick that was tipped over by Slovakia goalkeeper Matus Kozacik, and from the corner that followed Germany was in front. 

Kroos's delivery from the left was headed out by Milan Skriniar but the ball fell for Boateng on the edge of the box and the Bayern Munich stopper met it on the volley, finding the bottom-left corner with the aid of a small deflection off the unfortunate Skriniar. 

Slovakia was overwhelmed and conceded a penalty in the 13th minute when skipper Martin Skrtel grappled with Gomez as the two went for a high ball in the box. 

Skrtel was booked for his intervention, but Slovakia was let off the hook as Ozil's kick was well saved by Kozacik diving to his left. 

Excluding shootouts, it was the first penalty missed by a German player in a European championship finals match in open play. 

The miss did nothing to halt Germany's momentum, though, and it remained one-way traffic after that with Ozil fizzing a half-volley inches past as the ball dropped after Gomez and Jan Durica had gone up to contest another cross into the area.

Draxler shot wide on the turn from 18 yards before Jan Kozak's side finally worked Manuel Neuer four minutes prior to the break. 

Peter Pekarik's cross from the right found AC Milan midfielder Juraj Kucka six yards from goal but his header was tipped over the bar by the Germany captain. 

Germany went on to increase its lead two minutes after that as Draxler combined with Jonas Hector down the left before heading for the byline and cutting the ball back for Gomez to finish at the near post. 

Any hope of a contest in the second half depended on Slovakia quickly pulling a goal back but a neat 49th-minute move ended with Marek Hamsik — otherwise nullified as a threat — teeing up Kucka for a shot that went straight to Neuer. 

If there were any lingering doubts about the outcome, Germany put the game to bed on 63 minutes, Mats Hummels heading down a corner for Draxler, who volleyed in at the back post to get the goal his performance deserved.